US secretary of state Antony Blinken has sought to rally the spirits of Ukrainians facing a fierce new Russian offensive, assuring them they are not alone and that billions of dollars in American military aid on its way to the country will make a “real difference” on the battlefield.

After a day of meetings with senior officials, civil society figures and university students during which he exhorted them against being discouraged, Mr Blinken took to the stage at a Kyiv bar to play rhythm guitar with a local band on Neil Young’s 1989 hit Rockin’ In The Free World.

Earlier on his unannounced visit to Kyiv, Mr Blinken told Ukrainian leaders that despite a months-long delay in US assistance that left them vulnerable to renewed Russian military strikes, more weaponry is coming and some has already arrived.

Mr Blinken also lambasted Russian President Vladimir Putin for underestimating Ukraine’s determination to fight back.

“We meet at a critical moment,” he told students at the Kyiv Polytechnic Institute.

“The coming weeks and months will demand a great deal of Ukrainians, who have already sacrificed so much. I’ve come to Ukraine with a message: You are not alone.”

“We sometimes hear that time is on Putin’s side,” Mr Blinken said.

“That Russia’s bigger population, Putin’s willingness to throw more Russians into the meat grinder of his making and sink more of Russia’s resources into trying to subjugate Ukraine means that Russia can’t lose.

“In fact, Russia’s been losing the battle to control Ukraine’s destiny for 20 years. And Putin has it wrong – time is on Ukraine’s side.

“As the war goes on, Russia is going back in time. Ukraine is moving forward.”

Though most of those villages were already depopulated, thousands of civilians in the area have fled the fighting.

The Kremlin’s forces have also been making a concerted push in the east, seeking to drive deeper into the partly occupied Donetsk region.

The main focus of Russian attacks on Tuesday was Pokrovsk, just inside the Ukrainian border in Donetsk, where the Kremlin’s forces launched 24 assaults, the Ukrainian general staff said in a report.

Analysts have called this moment one of the most dangerous for Ukraine since Russia’s full-scale invasion in February 2022.

“We know this is a challenging time,” Mr Blinken told Mr Zelensky in his first meeting of the day after arriving in Kyiv on an overnight train from Poland.

But he added that American military aid is “going to make a real difference against the ongoing Russian aggression on the battlefield”.

The visit comes less than a month after Congress approved a long-delayed foreign assistance package that sets aside 60 billion dollars in aid for Ukraine, much of which will go towards replenishing badly depleted artillery and air defence systems.

More than 7,500 civilians have been evacuated from the area, according to authorities.

At the same time, the Kremlin’s forces are expanding their push to the northern border regions of Sumy and Chernihiv, Ukrainian officials say, and Kyiv’s outgunned and outnumbered soldiers are struggling to hold them back.

Troops fought street to street on the outskirts of Vovchansk, among the largest towns in the Kharkiv area, regional governor Oleh Syniehubov said on national television.

Two civilians were killed in Russian shelling on Tuesday, he said.

The UN human rights office said the battles are taking a heavy toll.

“We are deeply concerned at the plight of civilians in Ukraine,” Liz Throssell, spokeswoman for the office of the UN High Commissioner for Human Rights, said in Geneva.

“In the Kharkiv region, the situation is dire.”

The operator of the national high-voltage electricity grid, Ukrenergo, said late on Tuesday that it was starting “controlled emergency shutdowns” for industries and households because of “a significant shortage of electricity in the system due to Russian shelling and an increase in consumption due to the cold weather”.

Mr Zelensky thanked Mr Blinken for the US aid – but added that more is necessary, including two Patriot air defence systems urgently needed to protect Kharkiv.

“The people are under attack: civilians, warriors, everybody. They’re under Russian missiles,” he said.

Artillery, air defence interceptors and long-range ballistic missiles have already been delivered, some of them already to the front lines, said a senior US official travelling with the secretary.

Ahead of the trip, US officials noted that since President Joe Biden signed the aid package late last month, the administration has already announced 1.4 billion dollars in short-term military assistance and six billion dollars in longer-term support.

Mr Blinken, on his fourth trip to Kyiv since Russian troops rolled over the border, told Ukrainian prime minister Denys Shmyhal that the US intends to support Kyiv beyond the war’s end.

“The United States is determined, determined to help Ukraine succeed, succeed both in the battlefield victory but also succeed, as we would say, in winning the peace and building the strongest possible Ukraine,” Mr Blinken said.

Mr Blinken, for example, has visited the Middle East seven times since the war in Gaza began in October.

His last trip to Kyiv was in September.

Mr Blinken went with Ukrainian foreign minister Dmytro Kuleba for lunch at a Kyiv pizza restaurant founded by Ukrainian veterans, pronouncing it “superb”.

On Mr Blinken’s last visit, the pair ate at a recently reopened McDonald’s restaurant.